Spherical Motor Research Articles

Magnetic Field Coupling Analysis in Integrated Magnetic Suspension Spherical Induction Motors

Magnetic Field Coupling Analysis in Integrated Magnetic Suspension Spherical Induction Motors

Modeling and analysis of non-circumferential symmetric permanent magnet spherical motor using genetic algorithm-based torque map method.

A permanent magnet spherical motor (PMSpM) is a typical multiple-degree-of-freedom apparatus. This paper proposes a torque map-based torque model and its counterpart using a genetic algorithm for the PMSpM with non-circumferential symmetric permanent magnets. The basic structure and operating principle of the PMSpM under study are presented. The analytic model of the 3D magnetic field is researched using the spherical harmonic method. The magnetic field model is verified via finite element method (FEM) analysis and an experiment of radial magnetic flux density. The analytic torque model is formulated using the Lorentz force method. The torque maps are established according to the principle, and the torque map-based torque model originates from the maps. FEM and the experimental results prove the correctness of the torque map-based torque model, and real-time performance of the torque model is also estimated. To solve the coil current calculation difficulty, the genetic algorithm is introduced for establishing the reversal torque model; MATLAB simulation is conducted for the convergence speed of the reversal torque model; and the real-time performance is studied on Qt 5.14/C++ upper software.

End jitter suppression using FONFTSMC for rigid-flexible coupling systems of PMSpM based on NDO

A permanent magnet spherical motor (PMSpM) with three degrees of freedom rotation characteristics in the rigid rotor has broad application prospects. But the adding flexible material will inevitably produce end jitter issue in the process of the rigid-flexible coupling system (RFCs) movement. To solve the above problem, a fractional order non-singular fast terminal sliding mode control method with a disturbance observer was proposed for the rigid-flexible coupling system of a permanent magnet spherical motor (RFCs-PMSpM). Firstly, a dynamic model of RFCs-PMSpM was established by using the Hamilton principle and Euler–Bernoulli beam theory. Secondly, the influences on the end jitter were discussed from the perspectives of load mass, material parameters, and driving torque of the flexible shaft. The sensitivity analysis is carried out, and the key factors affecting the jitter are obtained. Then, a fractional order non-singular fast terminal sliding mode controller based on a nonlinear disturbance observer (NDO-FONFTSMC) is proposed. The stability of the closed-loop control system was proved by the Lyapunov method. Finally, the effectiveness of the proposed jitter suppression strategy was validated and compared with existing approaches, which also provides an important reference for the future application of RFCs-PMSpM in high-precision industry.

Electromagnetic torque modeling and validation for a permanent magnet spherical motor based on XGBoost

As a device characterized by multiple degrees of freedom in one driving unit, analytical electromagnetic torque modeling is needed for the rotor position tracking control of a Permanent Magnet Spherical Motor (PMSpM). In this paper, Extreme Gradient Boosting (XGBoost) was proposed to be employed for establishing the output relationship between the rotor position and the electromagnetic torque of PMSpM. The Finite Element Method (FEM) was applied to obtain train data and test data concerning the rotor position and electromagnetic torque of PMSpM. Particle Swarm Optimization (PSO) was applied to optimize partial parameters of XGBoost, which serves to enhance the modeling accuracy of electromagnetic torque via XGBoost. The predictive results of algorithms, including Random Forest (RF), Gradient Boosting Regression Tree (GBRT), Multi-task Gaussian Process (MTGP), and XGBoost, were compared with FEM results and experimental results over multiple indicators. The capability of XGBoost has been validated not only to perform modeling tasks within an abbreviated time span but also to generate models that display amplified accuracy and efficiency.

Omni-directional orientation analysis of a triplet-stator spherical piezoelectric motor system

ABSTRACT Spherical piezoelectric motors (SPMs) represent a promising actuator technology applicable to the development of motion control systems with multiple degrees of freedom. However, few SPMs have made it successfully to market, as an effective and systematic rotor orientation analysis and manipulation technique has yet to be developed. This study thus developed a novel triplet-stator SPM design that integrates electrode configuration to excite lateral vibrations and offers two fundamental rotor orientations for each set of piezoelectric plates by changing the contact position between the rotor and stator. To accomplish omnidirectional orientations for the proposed SPM system, we present a systematic orientation analysis based on spherical coordinates. We further apply the concept of vector composition to derive new composite orientations by adjusting the magnitude ratio of the provided torques between three stators. An orientation angle representation accounting for the rotor dynamics is used to validate the correctness of the synthesized orientation vectors both in simulation and experiments. The orientation analysis results in a three-dimensional sphere containing eight vector spaces corresponding to eight stator actuation modes, in which an arbitrary rotor orientation reference command can be generated under the designed actuation modes. Experimental results were well correlated with simulations, thereby verifying the effectiveness of the proposed SPM system design and orientation analysis.

A New Attitude Estimation Method for Spherical Reluctance Motor Based on Few Flux Linkage Samples

A New Attitude Estimation Method for Spherical Reluctance Motor Based on Few Flux Linkage Samples

Multi-DOF Orientation Detection of a Permanent Magnet Spherical Motor Based on Back EMF

Multi-DOF Orientation Detection of a Permanent Magnet Spherical Motor Based on Back EMF

Six Steps Commutation Torque and Dynamic Characteristics of Spherical Brushless Direct Current Motor

This paper presents developing a new three-degrees of freedom (DOF) electromagnetic actuator referred to here as a spherical brushless direct current (SBLDC) motor. The SBLDC motor consists of permanent magnets (PMs) in a rotor and three layers of electromagnets (EMs) in a stator. The EMs in the middle layer of the stator generate a spinning torque, and the other two layers, placed symmetrically with respect to the middle, produce a tilting torque. Winding layouts of the EMs in each layer are analytically studied for decoupling between spinning and tilting torque. Furthermore, a six steps commutation is proposed to independently control the tilting torque as well as the spinning torque. The commutation torque model is validated by the moment method based distributed multipoles (MMDMP) according to various tilting angles and directions. Then, the commutation torque model is further utilized to develop open-loop control and analyze stability with respect to equilibria. Finally, the performance of the SBLDC motor and control system is verified experimentally using commercial brushless direct current motor (BLDC) drivers. The results show the substantial potential of the SBLDC motor in automation and mobility applications requiring orientation control with high-speed spinning.

Modeling and optimization of a novel multi-DOF electromagnetic driven spherical motion generator

This paper introduces a new spherical motion generator and presents a method for modeling its magnetic field and analyzing its moments. The generator employs an electromagnetic drive of a spherical motor as its driving method and utilizes a spherical parallel manipulator to execute the spherical motion. The combination of these two technologies offers several advantages, including a large workspace and high motion accuracy. The equivalent magnetizing current method is used in the magnetic field modeling and the average air-gap flux density is optimized to achieve a better magnetic field distribution, and the accuracy of the analytical model is verified by finite element simulations and experiments.

Model and Property Analysis for a Ball-Hinged Three-Degree-of-Freedom Piezoelectric Spherical Motor.

Multi-degree-of-freedom piezoelectric motors have the advantages of high torque and resolution, simple structure, and direct drive, which are widely used in robot wrist joints, deep-sea mechanisms, medical equipment, and space mechanisms. To solve the problems of high force/torque coupling degree and ball low stator and rotor bonding strength of the traditional traveling wave type three-degree-of-freedom piezoelectric spherical motor, a new structure of ball-hinged piezoelectric spherical motor is proposed. Through coordinate transformation and force analysis, the driven mathematical model of the spherical motor is given. The model shows that the three degrees of freedom of the motor are coupled with each other. According to the mathematical model of the spherical motor, the mechanical properties of the motor are analyzed by the computer simulation. The results show that the stalling torque coefficient kt has a linear relationship with the friction coefficient ε and the stator preload Fc, has a nonlinear relationship with the stator radius R and the rotor radius r, and increases with the increase of R and decreases with the increase of r. The no-load speed of motor ωn is not related to the friction coefficient ε and the stator preload Fc, and increases with the increase of R and decreases with the increase of r. The anisotropic characteristics of torque and speed of a spherical motor are further analyzed, which lays a theoretical foundation for the drive control of a spherical motor.

A Variable Stiffness Spherical Joint Motor by Magnetic Energy Shaping

A Variable Stiffness Spherical Joint Motor by Magnetic Energy Shaping

Research on wireless power transmission of attitude detection system of MEMS sensor for spherical motor

Research on wireless power transmission of attitude detection system of MEMS sensor for spherical motor

Rotor Position Identification of Permanent Magnet Spherical Motor Based on Equilateral Spherical Triangles

Rotor Position Identification of Permanent Magnet Spherical Motor Based on Equilateral Spherical Triangles

Attitude measurement of permanent magnet spherical motors based on adaptive mahony complementary filtering

An adaptive attitude measurement algorithm called adaptive mahony complementary filter(AMCF) is proposed to address the issues of drift and noise in gyroscope measurements, as well as the high computational complexity, error accumulation, and sensitivity to noise in the quaternion extended kalman filter(QEKF) within the permanent magnet spherical motor(PMSM) inertial measurement unit. Firstly, this method corrects the gyroscope’s angular velocity bias by utilizing the error between theoretical and actual accelerations. Subsequently, the covariance is adjusted by comparing dynamic accelerations to mitigate disturbances. The fourth-order Runge-Kutta method is employed to continuously update the quaternion, thereby achieving higher accuracy in attitude measurement. Finally, static and dynamic experimental investigations are conducted on the PMSM. The experimental results demonstrate that the AMCF offers faster computation speed compared to the QEKF and higher accuracy than the fast complementary filtering(FCF). This indicates that utilizing the AMCF enables better real-time attitude measurement for three-degree-of-freedom mechanical structures.

Nonlinear optimal control for permanent magnet synchronous spherical motors

Nonlinear optimal control for permanent magnet synchronous spherical motors

Symmetric Nonlinear Feedback Control and Machine Learning for Sustainable Spherical Motor Operation

This paper presents a comprehensive evaluation of a new control technique for the sphere motor system, aimed at achieving accurate tracking, robust and dispersion of vibrations. Control methods include the determination of a nonlinear model and the application of feedback linearization, followed by the optimization of the proportional derivative (PD) coefficients through the Adaptive Neuro-Fuzzy Inference System. In addition, the system’s reaction to harsh environments is managed using Long Short-Term Memory. In order to gain a deeper understanding, symmetrical environmental disturbances and trajectories are introduced during the testing phase. The results demonstrate the superior performance of the control strategy, with reduced vibrations, faster recovery and confirmed tracking accuracy. In addition, the control method shows its adaptability and reliability, as evidenced by the significant reduction in CO2 emissions compared to conventional PD control methods. The use of symmetric trajectories and visualizations further emphasizes the behavior of the system under symmetric conditions, strengthening the effectiveness and applicability of the control strategy in real-world scenarios. Overall, this study presents a promising solution for converting complex systems under different conditions and making them potentially applicable in various industrial contexts.

Identification of Rotor Position of Permanent Magnet Spherical Motor Based on Compressed Sensing

The accurate identification of the rotor position of permanent magnet spherical motor (PMSM) is crucial to its closed-loop control. A novel method for rotor position identification of the PMSM based on compressive sensing is proposed, which can obtain accurate rotor position by a limited number of Hall sensors. Firstly, the paper designs a Hall sensor array based on the distribution characteristics of the rotor magnetic and the frequency domain characteristics of the air gap magnetic field, combined with the Fibonacci sequence. Then, an observation matrix construction method is proposed, used for compressed sensing of the radial magnetic field strength information in air gap. Finally, the position of the spherical rotor is identified according to the reconstructed information based on the sensor output value. The identification method is verified by experiments, which shows that the identification accuracy is about 1 degree.

A novel spherical ultrasonic motor with wire stators and measuring torque and preload via a new method.

The present study introduces a multi-degree-of-freedom (MDOF) ultrasonic motor, which is capable of driving a spherical rotor using spiral wire stators and a piezoelectric stack actuator. Wire stators and piezoelectric stack actuators enable the proposed motor to be smaller and simpler, lower in power consumption, and have different modes at different frequencies. In this motor, two wire stators are used to drive the spherical rotor and rotate it in different directions. The eigenfrequency and frequency domain analyses were carried out using the finite element method (FEM) to evaluate the MDOF capability of the motor in different vibration modes. It has been demonstrated that the piezoelectric stack actuator can provide MDOF motions through its vibration modes. The resonant frequency obtained by the frequency domain approach agreed with the impedance analyzer test. Rotational speed, torque, and preload force were experimentally investigated. Using shear stress caused by viscous fluid in contact with the spherical rotor, a new torque calculation method was developed. Based on the buoyancy force exerted on the immersed rotor, the preload force was measured. The experimental results indicated that the maximum rotational speed of the spherical rotor was 306rpm, and the maximum torque was 4.7 μNm.

Three-dimensional Interval Identification of Permanent Magnet Spherical Motor Based on Improved Deep Neural Network

Three-dimensional Interval Identification of Permanent Magnet Spherical Motor Based on Improved Deep Neural Network

A New Adaptive Analytical Model for the Spherical Reluctance Motor Based on Hybrid Trigonometric Function–Power Function

To realize the multiple-degree-of-freedom (multi-DOF) motion, this paper proposes a new spherical reluctance motor (SPRM). For the nonlinear characteristics of flux linkage and excessively complex torque calculation, this paper proposes a new adaptive analytical model for SPRM based on hybrid trigonometric function-power function. A sixth-degree polynomial is used to represent the five coefficients of this model, and these coefficients are calculated from flux linkage-rotor angle-phase current data using numerical curve fitting with nonlinear least square. Based on the criterion of minimizing the Sum of Squared Error (SSE) between the flux linkage obtained by Finite Element Analysis (FEA) and the flux linkage calculated by analytical model, the optimal trigonometric function angular frequency coefficient and the optimal power function exponent are adaptively obtained by iterative algorithm. The feasibility and accuracy of this model is validated by comparing with the existing models. Furthermore, the experimental results show that the calculated torque has a good agreement with the measured torque, which further verifies the validity of the proposed analytical model. The versatility of the proposed model for SPRMs with different structure parameters is discussed as well.